2003 Fiscal Year Final Research Report Summary
Research on constant mean curvature surfaces
| Project/Area Number |
12440012
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Tohoku University |
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Principal Investigator |
KENMOTSU Katsuei Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (60004404)
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| Co-Investigator(Kenkyū-buntansha) |
MASHIMO Katsuya Tokyo University of Agriculture and Technology, Professor, 工学部, 教授 (50157187)
NAGASAWA Takeyuki Saitama University, Faculty of Science, Professor, 理学部, 教授 (70202223)
NISHIKAWA Seiki Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (60004488)
TASAKI Hiroyuki Tsukuba University, Dep. of Math., Associate Professor, 数学系, 助教授 (30179684)
OHNITA Yoshihiro Tokyo Metropolitan University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (90183764)
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| Project Period (FY) |
2000 – 2003
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| Keywords | minimal surface / constant mean curvature surface / mean curvature vector / complex space form / periodic surface of revolution / Delaunay surface / Bezier curve / harmonic map |
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| Research Abstract |
1.We classified these isometric minimal immersions of real two dimensional Riemannian manifold with constant Gaussian curvature into a complex two dimensional complex space form. In this research, it was important to prove the constancy of the Kaehler angles of these immersions.
2.We studied periodic surfaces of revolution in the three dimensional Euclidean space in order to understand the importance of constant mean curvature surfaces and got the criterion for a periodic function to be the mean curvature of a periodic surface of revolution. Moreover, we found an interesting relation between periodic mean curvature function and Bezier curves.
3.Since the theory of non zero constant mean curvature surfaces is well developed on these twenty years, I have written a textbook about this subject in order to make a unified explanation of the theory. Recently, this book was translated into English by American Mathematical Society.
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